Trapezoid coordinate plane. A(2,1),B(3,4) C(9,4) D(12,1). Which of the vertical lines cuts ABCD into 2 trapezoids with equal areas?

Question

Area of Trapezoid = 1/2 h(b1 +b2)

Answer 1

I assume you're looking at a list of options, but as long as we know the line we want is vertical, there's only one option, so we can solve for it.  The top and bottom lengths are 6 and 10 and the height is 3, so total area is 

 

1/2 * 3 * (6+10) = 24

 

If we draw a vertical line at x = a and assess the area to the left, we have the same height, but our top and bottom lengths are (a-3) and (a-2).  So if want this area to be 12, we set

 

1/2 * 3 * (a-3 + a-2) = 12

(2a -5) = 8

2a = 13

a = 13/2 = 6.5

 

So, the vertical line we want is x = 6.5